Semiparametric joint models for longitudinal biomarkers and time to event data The goal of this project is to develop novel statistics methods to jointly model longitudinal biomarker trajectories and time to event data. The proposed methods are motivated and will be applied to three major applications: 1) liver transplant and kidney transplant available through the United Network for Organ Sharing (UNOS), 2) the end stage renal disease (ESRD) data available through the United States Renal Data System (USRDS), and 3) the Vaginal birth after a prior cesarean (VBAC) data collected at the University of Pennsylvania. The main motivation comes from the fact that biomarkers are usually the surrogates of the underlying disease process and need to be treated as surrogate outcomes in modeling the time to event data, and the trajectories of the biomarkers usually require nonparametric models allowing flexible patterns over time, such as smooth curves, shape-registered curves, and branching curves. Another motivation is that in predicting the event such as death, the cumulative effects of the biomarkers may be more appropriate than the concurrent values, and therefore we propose to combine the ideas of functional data analysis and survival analysis. We will first develop the functional accelerated failure time (AFT) models and their join models with functional mixed effects models. We then extend this framework to include non-Gaussian longitudinal biomarkers. The third specific aims will develop a series of nonlinear functional mixed effect models for curve registration and branching curves, and their joint models with time to event data. Each specific aim includes methods development, theoretical studies, empirical simulations and applications. We will also develop a user-friendly software package that includes all the proposed features and post it to public domain.